GUIpowermean

GUIpowermean shows the necessary calculations to obtain the power (generalized) mean in a GUI.

Syntax

Description

The power mean (also known as generalized mean, or Holder mean or Kolmogorov-Negumo function of the mean), is an abstraction of the Pythagorean means. It includes the harmonic $(s=-1)$, geometric ($s\rightarrow 0$), and arithmetic ($s=1$), quadratic ($s=2$), cubic mean ($s=3$). When $s \rightarrow -\infty$ the power mean tends to $x_{min}$ and when $s\rightarrow +\infty$ the power mean tends to $x_{max}$. http://en.wikipedia.org/wiki/Generalized_mean

example

out =GUIpowermean(x, s) Example of use of the cubic mean.

example

out =GUIpowermean(x, s, w) Example of use of weighted geometric mean.

Examples

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  • Example of use of the cubic mean.
  • See page 92 of [MRZ]

    x=[60 30 50 50  80 35000  80 95];
    out=GUIpowermean(x,3);
    Click here for the graphical output of this example (link to Ro.S.A. website). Graphical output could not be included in the installation file because toolboxes cannot be greater than 20MB. To load locally the image files, download zip file http://rosa.unipr.it/fsda/images.zip and unzip it to <tt>(docroot)/FSDA/images</tt> or simply run routine <tt>downloadGraphicalOutput.m</tt>

  • Example of use of weighted geometric mean.
  • See page 82 of [MRZ]

    x=[1.01 1.02 1.03];
    w=[2 6 4];
    out=GUIpowermean(x,0,w);
    Click here for the graphical output of this example (link to Ro.S.A. website). Graphical output could not be included in the installation file because toolboxes cannot be greater than 20MB. To load locally the image files, download zip file http://rosa.unipr.it/fsda/images.zip and unzip it to <tt>(docroot)/FSDA/images</tt> or simply run routine <tt>downloadGraphicalOutput.m</tt>

    Input Arguments

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    x — vector of numeric data. Vector.

    Vector containing strictly numerical data.

    Data Types: double

    s — power indicator. Scalar.

    Power indicator for the desired mean ($s=- \inf= x_{min}$; $s=-1$ harmonic mean; $s=0$ geometric mean; $s=1$ = arithmetic mean; $s=2$ quadratic mean; $s=3$ cubic mean, $s=+\inf$ = $x_{max}$).

    Example - 1:10

    Data Types: double

    Optional Arguments

    w — weights. Vector.

    Vector of the same length of x containing the weights assigned to each observation. If w is not supplied we assume that all observations have weight equal to 1.

    Example: 1:10

    Data Types: double

    Output Arguments

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    out —detailed output to compute the index. Table

    Table with n+1 rows (where n is the length of x) containing what is shown in the GUI. Last row contains the totals.

    References

    Milioli, M.A., Riani, M., Zani, S. (2019), "Introduzione all'analisi dei dati statistici (Quarta edizione ampliata)". [MRZ]

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